Proximal methods for point source localisation
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914676473856000 |
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| author | Valkonen, Tuomo |
| author_facet | Valkonen, Tuomo |
| contents | Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical algorithms for point source localisation are based on the Frank-Wolfe conditional gradient method, for which ad hoc convergence theory is developed. We develop extensions of proximal-type methods to spaces of measures. This includes forward-backward splitting, its inertial version, and primal-dual proximal splitting. Their convergence proofs follow standard patterns. We demonstrate their numerical efficacy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_02991 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Proximal methods for point source localisation Valkonen, Tuomo Optimization and Control Computer Vision and Pattern Recognition Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical algorithms for point source localisation are based on the Frank-Wolfe conditional gradient method, for which ad hoc convergence theory is developed. We develop extensions of proximal-type methods to spaces of measures. This includes forward-backward splitting, its inertial version, and primal-dual proximal splitting. Their convergence proofs follow standard patterns. We demonstrate their numerical efficacy. |
| title | Proximal methods for point source localisation |
| topic | Optimization and Control Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2212.02991 |